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3 years ago

8. What are the advantages of switching a quadratic function from standard form into vertex form?

Mathematics

1 answer:

Airida [17]3 years ago

3 0

Answer:

vertex form automatically gives you your vertex and your y intercept so all you need to do is graph. Hope this helps

Step-by-step explanation:

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Let φ(x, y) = arctan (y/x) .

Alexandra [31]

Answer:

a) $\large F(x,y)=(-\frac{y}{x^2+y^2},\frac{x}{x^2+y^2})$

b) $\large \mathbb{R}^2-\{(0,0)\}$

c) the points of the form (x, -x) for x≠0

Step-by-step explanation:

If φ(x, y) = arctan (y/x), the vector field F = ∇φ would be

$\large F(x,y)=(\frac{\partial \phi}{\partial x},\frac{\partial \phi}{\partial y})$

On one hand we have,

$\large \frac{\partial \phi}{\partial x}=\frac{\partial arctan(y/x)}{\partial x}=\frac{-y/x^2}{1+(y/x)^2}=-\frac{y/x^2}{1+y^2/x^2}=\\\\=-\frac{y/x^2}{(x^2+y^2)/x^2}=-\frac{y}{x^2+y^2}$

On the other hand,

$\large \frac{\partial \phi}{\partial y}=\frac{\partial arctan(y/x)}{\partial y}=\frac{1/x}{1+(y/x)^2}=\frac{1/x}{1+y^2/x^2}=\\\\=\frac{1/x}{(x^2+y^2)/x^2}=\frac{x}{x^2+y^2}$

$\large F(x,y)=(-\frac{y}{x^2+y^2},\frac{x}{x^2+y^2})$

The domain of definition of F is

$\large \mathbb{R}^2-\{(0,0)\}$

i.e., all the plane X-Y except the (0,0)

Here we want to find all the points such that

$\large (-\frac{y}{x^2+y^2},\frac{x}{x^2+y^2})=(k,k)$

where k is a real number other than 0.

But this means

$\large -\frac{y}{x^2+y^2}=\frac{x}{x^2+y^2}\Rightarrow y=-x$

So, all the points in the line y = -x except (0,0) are parallel to the vector field F, that is, the points (x, -x) with x≠ 0

8 0

2 years ago

Felicity baby sat 2 hours each night for 10 nights. She earned a total of $180 babysitting. Felicity wants to calculate her hou

natulia [17]

Answer:

To find Felicity's hourly rate you first want to find out how many hours she has babysat altogether. In order to do this we need to take 2*10=20

With that 20 we can divide it by 180 to find her hourly rate

180/20= 9

So she makes $9 an hour

Step-by-step explanation:

7 0

2 years ago

kofi and kojo were given 380 to share .kojo had 75 more than kofi. If kofi share is x find an expression for kojo share

AleksAgata [21]

Answer:

227.5

Step-by-step explanation:

x=Kofi

x+75=Kojo

x+x+75=380

2x+75=380

2x=305

x=152.5

Kojo=152.5 plus 75

227.5

4 0

2 years ago

Order the fractions from least to greatest.<br> 1<br> -1.25, 0.125,<br> 1<br> 4

liberstina [14]

Answer:

-1.25, -1/4, -1/8, 0.125

Step-by-step explanation:

5 0

2 years ago

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Nick's bank account balance was $21. if he writes a check for $30 and his bank charges him $35 for overdrawing his account, find

natulia [17]

It is saying that the Balance was 21 if he wrote a check for 30 and The bank was charging him $35 for overdrawing his account of basically you’re gonna just Add so 21+30+35 is 86

4 0

3 years ago

Read 2 more answers